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Sezgin Akbulut

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Abdul Rahman Khan

HeNan Normal University

Abdul Qayyum Khan

Pakistan Institute of engineering and applied science (PIEAS)

Izhar Uddin (Asstt. Prof., D/o Mathematics)

Jamia Millia Islamia

Mihai Postolache

University Politehnica of Bucharest

King AbdulAziz University (KAU) Jeddah, Saudi Arabia

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Papers by Sezgin Akbulut

Some common-fixed-point-results for nonself asymptotically qausi-nonexpansive mappings by a two-step iterative process

by Safeer H Khan and Sezgin Akbulut

Strong convergence results for two asymptotically quasinonexpansive mappings are obtained by usin... more Strong convergence results for two asymptotically quasinonexpansive mappings are obtained by using a general and independent two-step iterative process assuming compactness of only one of the two mappings and then under the condition (A ). Weak convergence is obtained under Opial's condition. Our results generalize a number of corresponding results in contemporary literature. Another interseting fact is that our results obtained even for only one mapping are new.

Strong convergence of an explicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces

Miskolc Mathematical Notes

In this paper, we study strong convergence of an iteration process for a finite family of asympto... more In this paper, we study strong convergence of an iteration process for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces. We prove some strong convergence theorems for this iterative algorithm. Our results improve and extend the corresponding results of Kettapun et al. .

Strong and �-Convergence Theorems in Hyperbolic Spaces

Miskolc Mathematical Notes

In this paper, we prove some strong and -convergence theorems for two finite families of nonexpan... more In this paper, we prove some strong and -convergence theorems for two finite families of nonexpansive maps on a hyperbolic space. Our iterative scheme is independent and simpler than the Ishikawa type iteration process. Our results refine and generalize several recent and comparable results in uniformly convex Banach spaces as well as CAT(0) spaces.

On the generalized Whitney sum of the sheaves of the fundamental groups

Let X 1 ,X 2 ,⋯,X n be connected and locally path connected topological spaces and H 1 ,H 2 ,⋯,H ... more Let X 1 ,X 2 ,⋯,X n be connected and locally path connected topological spaces and H 1 ,H 2 ,⋯,H n be the sheaves of fundamental groups on X 1 ,X 2 ,⋯,X n , respectively. In this paper, we first construct the sheaf H ⊕ =H 1 ⊕H 2 ⊕⋯⊕H n by defining a “Generalized Whitney Sum” and the sheaf H × =∏ i=1 n H 1 ×H 2 ×⋯×H n which is the direct sum of the sheaves H 1 ,H 2 ,⋯,⋯,H n . Finally, we prove that if (X 1 ,H 1 ),(X 2 ,H 2 ),⋯,(X n ,H n ) are any pairs, then the sheaf H ⊕ is isomorphic to the sheaf H × on X 1 ×X 2 ×⋯×X n .

Common Fixed Points of A Finite Family of I-Asymptotically Nonexpansive Mappings By S-iteration Process In Banach Spaces

In this paper, we consider S iteration process to approximate the common fixed points of a finite... more In this paper, we consider S iteration process to approximate the common fixed points of a finite family of I-asymptotically nonexpansive mappings in Banach spaces. We also study the different convergence criteria of S iteration process under some suitable conditions. It presents some new results in this paper.

Picard iteration converges faster than Noor iteration for a class of quasi-contractive operators

Chiang Mai Journal of Science

The purpose of this paper is to introduce that Noor (three-step) iteration converges strongly to ... more

On the equivalence of some fixed point iterations

Kyungpook Mathematical Journal

The equivalence of the Mann, Ishikawa, and Noor iteration procedures is established for a special... more The equivalence of the Mann, Ishikawa, and Noor iteration procedures is established for a special class of Lipschitzian operators on a closed, convex subset of a Banach space. The results are proved in arbitrary Banach spaces. A suitable example is given to illustrate the theorem. The results are interesting and will be particularly useful to experts in fixed point theory.

Solving nonlinear φ-strongly accretive operator equations by a one-step-two-mappings iterative scheme

by Safeer H Khan and Sezgin Akbulut

A solution of nonlinear -strongly accretive operator equations is found in this paper by using a ... more A solution of nonlinear -strongly accretive operator equations is found in this paper by using a one-step-two-mappings iterative scheme in arbitrary real Banach spaces. We give an example to validate our main theorem. Our results are different from those of Khan et. al., [S. H. Khan, A. Rafiq, N. Hussain, Fixed Point Theory Appl., 2012 (2012), 10 pages] in view of different and independent iterative schemes in the sense that none reduces to the other but extend and improve the results of Ding [X. P. Ding, Computers Math. Appl., 33 (1997), 75{82] and many others.

Convergence Theorems of a New Three-Step Iteration for Nonself Asymptotically Nonexpansive Mappings

On convergence of an implicit iterative algorithm for non self asymptotically non expansive mappings

by Safeer H Khan and Sezgin Akbulut

In this paper, we study an implicit iterative algorithm for two finite families of nonself asympt... more In this paper, we study an implicit iterative algorithm for two finite families of nonself asymptotically nonexpansive mappings. We prove some weak and strong convergence theorems for this iterative algorithm. Our results improve and extend the corresponding results of Soltuz [4], Xu and Ori [5], Khan et al. .

Growth Inhibition of Ralstonia solanacearum PT1J by Antagonistic Bacteria Isolated from Soils in the Northern Part of Thailand

An iteration process for common fixed points of two nonself asymptotically nonexpansive mappings

by Sezgin Akbulut and Safeer H Khan

Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2012

In this paper, we introduce an iteration process for approximating common fixed points of two non... more In this paper, we introduce an iteration process for approximating common fixed points of two nonself asymptotically nonexpansive mappings in Banach spaces. Our process contains Mann iteration process and some other processes for nonself mappings but is independent of Ishikawa iteration process. We prove some weak and strong convergence theorems for this iteration process. Our results generalize and improve some results in contemporary literature.

Some Subclasses of Close-to-Convex and Quasi-Convex Functions with Respect to k-Symmetric Points1

by Zhi-Gang Wang and Sezgin Akbulut

In the present paper, the authors introduce two new subclasses C(k)(¸, ®) of close-to-convex func... more In the present paper, the authors introduce two new subclasses C(k)(¸, ®) of close-to-convex functions and QC(k)(¸, ®) of quasi-convex functions with respect to k-symmetric points. The integral represen- tations and convolution conditions for these classes are provided. Some coefficient inequalities for functions belonging to thes e classes and their subclasses with negative coefficients are also provi ded.

WITHDRAWN: A two-step iterative process for common fixed points in Banach spaces

by Murat Ozdemir and Sezgin Akbulut

Journal of Computational and Applied Mathematics, 2012

On Common Fixed Points of Two Non-self Nonexpansive Mappings in Banach Spaces

Suppose that K is a nonempty closed convex subset of a real uniformly convex Banach space E with ... more

A New Two-Step Iterative Process with Errors for Common Fixed Points in Banach Spaces

by Murat Ozdemir and Sezgin Akbulut

Selçuk Journal of Applied Mathematics

Abstract: In this paper, a new two-step iterative scheme with errors is introduced for two asympt... more

Convergence Theorems on a New Iteration Process for Two Asymptotically Nonexpansive Nonself-Mappings with Errors in Banach Spaces

Discrete Dynamics in Nature and Society, 2010

We introduce a new two-step iterative scheme for two asymptotically nonexpansive nonselfmappings ... more We introduce a new two-step iterative scheme for two asymptotically nonexpansive nonselfmappings in a uniformly convex Banach space. Weak and strong convergence theorems are established for this iterative scheme in a uniformly convex Banach space. The results presented extend and improve the corresponding results of Chidume et al.

Common Fixed Points for Two Nonexpansive Nonself-Mappings with Errors in Banach Spaces

… for Science and …, 2010

... for all t A ð0, yÞ such that kx À Txk bf ðdðx, FðTÞÞÞ for all x AK where dðx, FðTÞÞ ¼ inffkx ... more

Diagonal Lift in the Cotangent Bundle and its Applications

by Murat Ozdemir and Sezgin Akbulut

Turkish Journal of Mathematics, 2001

The purpose of this paper is to define a diagonal lift D g of a Riemannian metric g of a manifold... more

On the subclass of p-valently functions

by Murat Ozdemir and Sezgin Akbulut

Applied Mathematics and Computation, 2004

Using the Salagean derivative, we introduce and study a class of p-valently functions with negati... more

Some common-fixed-point-results for nonself asymptotically qausi-nonexpansive mappings by a two-step iterative process

by Safeer H Khan and Sezgin Akbulut

Strong convergence results for two asymptotically quasinonexpansive mappings are obtained by usin... more Strong convergence results for two asymptotically quasinonexpansive mappings are obtained by using a general and independent two-step iterative process assuming compactness of only one of the two mappings and then under the condition (A ). Weak convergence is obtained under Opial's condition. Our results generalize a number of corresponding results in contemporary literature. Another interseting fact is that our results obtained even for only one mapping are new.

Strong convergence of an explicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces

Miskolc Mathematical Notes

In this paper, we study strong convergence of an iteration process for a finite family of asympto... more In this paper, we study strong convergence of an iteration process for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces. We prove some strong convergence theorems for this iterative algorithm. Our results improve and extend the corresponding results of Kettapun et al. .

Strong and �-Convergence Theorems in Hyperbolic Spaces

Miskolc Mathematical Notes

In this paper, we prove some strong and -convergence theorems for two finite families of nonexpan... more In this paper, we prove some strong and -convergence theorems for two finite families of nonexpansive maps on a hyperbolic space. Our iterative scheme is independent and simpler than the Ishikawa type iteration process. Our results refine and generalize several recent and comparable results in uniformly convex Banach spaces as well as CAT(0) spaces.

On the generalized Whitney sum of the sheaves of the fundamental groups

Let X 1 ,X 2 ,⋯,X n be connected and locally path connected topological spaces and H 1 ,H 2 ,⋯,H ... more Let X 1 ,X 2 ,⋯,X n be connected and locally path connected topological spaces and H 1 ,H 2 ,⋯,H n be the sheaves of fundamental groups on X 1 ,X 2 ,⋯,X n , respectively. In this paper, we first construct the sheaf H ⊕ =H 1 ⊕H 2 ⊕⋯⊕H n by defining a “Generalized Whitney Sum” and the sheaf H × =∏ i=1 n H 1 ×H 2 ×⋯×H n which is the direct sum of the sheaves H 1 ,H 2 ,⋯,⋯,H n . Finally, we prove that if (X 1 ,H 1 ),(X 2 ,H 2 ),⋯,(X n ,H n ) are any pairs, then the sheaf H ⊕ is isomorphic to the sheaf H × on X 1 ×X 2 ×⋯×X n .

Common Fixed Points of A Finite Family of I-Asymptotically Nonexpansive Mappings By S-iteration Process In Banach Spaces

In this paper, we consider S iteration process to approximate the common fixed points of a finite... more In this paper, we consider S iteration process to approximate the common fixed points of a finite family of I-asymptotically nonexpansive mappings in Banach spaces. We also study the different convergence criteria of S iteration process under some suitable conditions. It presents some new results in this paper.

Picard iteration converges faster than Noor iteration for a class of quasi-contractive operators

Chiang Mai Journal of Science

The purpose of this paper is to introduce that Noor (three-step) iteration converges strongly to ... more

On the equivalence of some fixed point iterations

Kyungpook Mathematical Journal

The equivalence of the Mann, Ishikawa, and Noor iteration procedures is established for a special... more The equivalence of the Mann, Ishikawa, and Noor iteration procedures is established for a special class of Lipschitzian operators on a closed, convex subset of a Banach space. The results are proved in arbitrary Banach spaces. A suitable example is given to illustrate the theorem. The results are interesting and will be particularly useful to experts in fixed point theory.

Solving nonlinear φ-strongly accretive operator equations by a one-step-two-mappings iterative scheme

by Safeer H Khan and Sezgin Akbulut

A solution of nonlinear -strongly accretive operator equations is found in this paper by using a ... more A solution of nonlinear -strongly accretive operator equations is found in this paper by using a one-step-two-mappings iterative scheme in arbitrary real Banach spaces. We give an example to validate our main theorem. Our results are different from those of Khan et. al., [S. H. Khan, A. Rafiq, N. Hussain, Fixed Point Theory Appl., 2012 (2012), 10 pages] in view of different and independent iterative schemes in the sense that none reduces to the other but extend and improve the results of Ding [X. P. Ding, Computers Math. Appl., 33 (1997), 75{82] and many others.

Convergence Theorems of a New Three-Step Iteration for Nonself Asymptotically Nonexpansive Mappings

On convergence of an implicit iterative algorithm for non self asymptotically non expansive mappings

by Safeer H Khan and Sezgin Akbulut

In this paper, we study an implicit iterative algorithm for two finite families of nonself asympt... more In this paper, we study an implicit iterative algorithm for two finite families of nonself asymptotically nonexpansive mappings. We prove some weak and strong convergence theorems for this iterative algorithm. Our results improve and extend the corresponding results of Soltuz [4], Xu and Ori [5], Khan et al. .

Growth Inhibition of Ralstonia solanacearum PT1J by Antagonistic Bacteria Isolated from Soils in the Northern Part of Thailand

An iteration process for common fixed points of two nonself asymptotically nonexpansive mappings

by Sezgin Akbulut and Safeer H Khan

Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2012

In this paper, we introduce an iteration process for approximating common fixed points of two non... more In this paper, we introduce an iteration process for approximating common fixed points of two nonself asymptotically nonexpansive mappings in Banach spaces. Our process contains Mann iteration process and some other processes for nonself mappings but is independent of Ishikawa iteration process. We prove some weak and strong convergence theorems for this iteration process. Our results generalize and improve some results in contemporary literature.

Some Subclasses of Close-to-Convex and Quasi-Convex Functions with Respect to k-Symmetric Points1

by Zhi-Gang Wang and Sezgin Akbulut

In the present paper, the authors introduce two new subclasses C(k)(¸, ®) of close-to-convex func... more In the present paper, the authors introduce two new subclasses C(k)(¸, ®) of close-to-convex functions and QC(k)(¸, ®) of quasi-convex functions with respect to k-symmetric points. The integral represen- tations and convolution conditions for these classes are provided. Some coefficient inequalities for functions belonging to thes e classes and their subclasses with negative coefficients are also provi ded.

WITHDRAWN: A two-step iterative process for common fixed points in Banach spaces

by Murat Ozdemir and Sezgin Akbulut

Journal of Computational and Applied Mathematics, 2012

On Common Fixed Points of Two Non-self Nonexpansive Mappings in Banach Spaces

Suppose that K is a nonempty closed convex subset of a real uniformly convex Banach space E with ... more

A New Two-Step Iterative Process with Errors for Common Fixed Points in Banach Spaces

by Murat Ozdemir and Sezgin Akbulut

Selçuk Journal of Applied Mathematics

Abstract: In this paper, a new two-step iterative scheme with errors is introduced for two asympt... more

Convergence Theorems on a New Iteration Process for Two Asymptotically Nonexpansive Nonself-Mappings with Errors in Banach Spaces

Discrete Dynamics in Nature and Society, 2010

We introduce a new two-step iterative scheme for two asymptotically nonexpansive nonselfmappings ... more We introduce a new two-step iterative scheme for two asymptotically nonexpansive nonselfmappings in a uniformly convex Banach space. Weak and strong convergence theorems are established for this iterative scheme in a uniformly convex Banach space. The results presented extend and improve the corresponding results of Chidume et al.

Common Fixed Points for Two Nonexpansive Nonself-Mappings with Errors in Banach Spaces

… for Science and …, 2010

... for all t A ð0, yÞ such that kx À Txk bf ðdðx, FðTÞÞÞ for all x AK where dðx, FðTÞÞ ¼ inffkx ... more

Diagonal Lift in the Cotangent Bundle and its Applications

by Murat Ozdemir and Sezgin Akbulut

Turkish Journal of Mathematics, 2001

The purpose of this paper is to define a diagonal lift D g of a Riemannian metric g of a manifold... more

On the subclass of p-valently functions

by Murat Ozdemir and Sezgin Akbulut

Applied Mathematics and Computation, 2004

Using the Salagean derivative, we introduce and study a class of p-valently functions with negati... more