Let K be a nonempty, closed and convex subset of a real Banach space E. Let T : K ! K be a strict... more Let K be a nonempty, closed and convex subset of a real Banach space E. Let T : K ! K be a strictly pseudocontractive map in the sense of Browder and Petryshyn. For a fixed x 0 2 K, define a sequence fx n g by x nþ1 ¼ ð1 À a n Þx n þ a n Tx n ;
We obtain necessary conditions for the existence of fixed point and approximate fixed point of no... more We obtain necessary conditions for the existence of fixed point and approximate fixed point of nonexpansive and quasi nonexpansive maps defined on a compact convex subset of a uniformly convex complete metric space. We obtain results on best approximation as a fixed point in a strictly convex metric space.
Sufficient conditions for the existence of a common fixed point for uniformly C q − commuting map... more Sufficient conditions for the existence of a common fixed point for uniformly C q − commuting mappings satisfying a generalized contractive conditions in the framework of a convex metric space are obtained. As an application, related results on best approximation are derived. Our results generalize various known results in the literature.
International Journal of Mathematics and Mathematical Sciences, 2009
Existence of common fixed point for two mappings which satisfy a generalized weak contractive con... more Existence of common fixed point for two mappings which satisfy a generalized weak contractive condition is established. As a consequence, a common fixed point result for mappings satisfying a contractive condition of integral type is obtained. Our results generalize, extend, and unify several well-known comparable results in literature.
Rendiconti Del Circolo Matematico Di Palermo, 2010
In this paper, we introduce a new one-step iterative process to approximate the common fixed poin... more In this paper, we introduce a new one-step iterative process to approximate the common fixed points of two multivalued nonexpansive mappings. We will also prove a strong convergence theorem in a uniformly convex Banach space under the multivalued version of so-called Condition (A′).
The purpose of this paper is to introduce the notion of common limit range property (CLR property... more The purpose of this paper is to introduce the notion of common limit range property (CLR property) for two hybrid pairs of mappings in fuzzy metric spaces, and we prove common fixed point theorems using (CLR) property for these mappings with implicit relation. Our results extend some known results to multi-valued arena. Also, we prove common fixed point theorem in fuzzy metric spaces satisfying an integral type.
Results regarding the existence of random fixed points of a nonexpansive random operator defined ... more Results regarding the existence of random fixed points of a nonexpansive random operator defined on an unbounded subset of a Banach space are proved.
The existence of coincidence points and common fixed points for four mappings satisfying generali... more The existence of coincidence points and common fixed points for four mappings satisfying generalized contractive conditions without exploiting the notion of continuity of any map involved therein, in a cone metric space is proved. These results extend, unify and generalize several well known comparable results in the existing literature.
Journal of Applied Mathematics and Computing, 2007
We iteratively generate a sequence of measurable mappings and study necessary conditions for its ... more We iteratively generate a sequence of measurable mappings and study necessary conditions for its convergence to a random fixed point of random nonexpansive operator. A random fixed point theorem for random nonexpansive operator, relaxing the convexity condition on the underlying space, is also proved. As an application, we obtained random fixed point theorems for Caristi type random operators.
Several fixed point theorems for hybrid pairs of single-valued and multivalued occasionally weakl... more Several fixed point theorems for hybrid pairs of single-valued and multivalued occasionally weakly compatible maps satisfying generalized contractive conditions are established in a symmetric space.
A notion of generalized cone metric space is introduced, and some convergence properties of seque... more A notion of generalized cone metric space is introduced, and some convergence properties of sequences are proved. Also some fixed point results for mappings satisfying certain contractive conditions are obtained. Our results complement, extend and unify several well known results in the literature. , G(a, b, b) Note that X is nonsymmetric G−cone metric space as G .
Coupled common fixed point Coupled coincidence point Coupled point of coincidence Cone metric spa... more Coupled common fixed point Coupled coincidence point Coupled point of coincidence Cone metric space Normal and non-normal cone a b s t r a c t
In this paper we demonstrate that a number of fixed point iteration problems can be solved using ... more In this paper we demonstrate that a number of fixed point iteration problems can be solved using a modified Krasnoselskij iteration process, which is much simpler to use than the other iteration schemes that have been defined.
In this paper, study of necessary conditions for the existence of unique coupled common fixed poi... more In this paper, study of necessary conditions for the existence of unique coupled common fixed point of contractive type mappings in the context of two generalized metric spaces is initiated. These results generalize several comparable results from the current literature. We also provide illustrative examples in support of our new results.
Common fixed point theorems for the class of four non compatible mappings in fuzzy metric spaces ... more Common fixed point theorems for the class of four non compatible mappings in fuzzy metric spaces are proved. These results are proved without exploiting the notion of continuity and without imposing any condition on t-norm. * Mathematics Subject Classifications: 54H25,47H10,54E40,54E35.
We use an iteration scheme to approximate common fixed points of nearly asymptotically nonexpansi... more We use an iteration scheme to approximate common fixed points of nearly asymptotically nonexpansive mappings. We generalize corresponding theorems of [1] to the case of two nearly asymptotically nonexpansivemappings and those of [9] not only to a larger class of mappings but also with better rate of convergence.
We prove the existence of fuzzy common fixed point of two mappings satisfying a generalized contr... more We prove the existence of fuzzy common fixed point of two mappings satisfying a generalized contractive condition in complete ordered spaces. Our results provide extension as well as substantial improvements of several well-known results in the existing literature and initiate the study of fuzzy fixed point theorems in ordered spaces.
In this paper, we introduce an iteration scheme for two multivalued maps in Kohlenbach hyperbolic... more In this paper, we introduce an iteration scheme for two multivalued maps in Kohlenbach hyperbolic spaces. This extends the single-valued iteration process due to Agarwal et al. (J. Nonlinear Convex Anal. 8(1):61-79, 2007). Using this new algorithm, we approximate common fixed points of two multivalued mappings through -convergence and strong convergence under some weaker conditions. A necessary and sufficient condition is given for strong convergence. MSC: Primary 47A06; 47H09; 47H10; secondary 49M05
In this paper, we introduce the notion of almost generalized (ψ , ϕ) s -contractive mappings and ... more In this paper, we introduce the notion of almost generalized (ψ , ϕ) s -contractive mappings and we establish some fixed and common fixed point results for this class of mappings in ordered complete b-metric spaces. Our results generalize several well-known comparable results in the literature. Finally, two examples support our results. MSC: 54H25; 47H10; 54E50
Let K be a nonempty, closed and convex subset of a real Banach space E. Let T : K ! K be a strict... more Let K be a nonempty, closed and convex subset of a real Banach space E. Let T : K ! K be a strictly pseudocontractive map in the sense of Browder and Petryshyn. For a fixed x 0 2 K, define a sequence fx n g by x nþ1 ¼ ð1 À a n Þx n þ a n Tx n ;
We obtain necessary conditions for the existence of fixed point and approximate fixed point of no... more We obtain necessary conditions for the existence of fixed point and approximate fixed point of nonexpansive and quasi nonexpansive maps defined on a compact convex subset of a uniformly convex complete metric space. We obtain results on best approximation as a fixed point in a strictly convex metric space.
Sufficient conditions for the existence of a common fixed point for uniformly C q − commuting map... more Sufficient conditions for the existence of a common fixed point for uniformly C q − commuting mappings satisfying a generalized contractive conditions in the framework of a convex metric space are obtained. As an application, related results on best approximation are derived. Our results generalize various known results in the literature.
International Journal of Mathematics and Mathematical Sciences, 2009
Existence of common fixed point for two mappings which satisfy a generalized weak contractive con... more Existence of common fixed point for two mappings which satisfy a generalized weak contractive condition is established. As a consequence, a common fixed point result for mappings satisfying a contractive condition of integral type is obtained. Our results generalize, extend, and unify several well-known comparable results in literature.
Rendiconti Del Circolo Matematico Di Palermo, 2010
In this paper, we introduce a new one-step iterative process to approximate the common fixed poin... more In this paper, we introduce a new one-step iterative process to approximate the common fixed points of two multivalued nonexpansive mappings. We will also prove a strong convergence theorem in a uniformly convex Banach space under the multivalued version of so-called Condition (A′).
The purpose of this paper is to introduce the notion of common limit range property (CLR property... more The purpose of this paper is to introduce the notion of common limit range property (CLR property) for two hybrid pairs of mappings in fuzzy metric spaces, and we prove common fixed point theorems using (CLR) property for these mappings with implicit relation. Our results extend some known results to multi-valued arena. Also, we prove common fixed point theorem in fuzzy metric spaces satisfying an integral type.
Results regarding the existence of random fixed points of a nonexpansive random operator defined ... more Results regarding the existence of random fixed points of a nonexpansive random operator defined on an unbounded subset of a Banach space are proved.
The existence of coincidence points and common fixed points for four mappings satisfying generali... more The existence of coincidence points and common fixed points for four mappings satisfying generalized contractive conditions without exploiting the notion of continuity of any map involved therein, in a cone metric space is proved. These results extend, unify and generalize several well known comparable results in the existing literature.
Journal of Applied Mathematics and Computing, 2007
We iteratively generate a sequence of measurable mappings and study necessary conditions for its ... more We iteratively generate a sequence of measurable mappings and study necessary conditions for its convergence to a random fixed point of random nonexpansive operator. A random fixed point theorem for random nonexpansive operator, relaxing the convexity condition on the underlying space, is also proved. As an application, we obtained random fixed point theorems for Caristi type random operators.
Several fixed point theorems for hybrid pairs of single-valued and multivalued occasionally weakl... more Several fixed point theorems for hybrid pairs of single-valued and multivalued occasionally weakly compatible maps satisfying generalized contractive conditions are established in a symmetric space.
A notion of generalized cone metric space is introduced, and some convergence properties of seque... more A notion of generalized cone metric space is introduced, and some convergence properties of sequences are proved. Also some fixed point results for mappings satisfying certain contractive conditions are obtained. Our results complement, extend and unify several well known results in the literature. , G(a, b, b) Note that X is nonsymmetric G−cone metric space as G .
Coupled common fixed point Coupled coincidence point Coupled point of coincidence Cone metric spa... more Coupled common fixed point Coupled coincidence point Coupled point of coincidence Cone metric space Normal and non-normal cone a b s t r a c t
In this paper we demonstrate that a number of fixed point iteration problems can be solved using ... more In this paper we demonstrate that a number of fixed point iteration problems can be solved using a modified Krasnoselskij iteration process, which is much simpler to use than the other iteration schemes that have been defined.
In this paper, study of necessary conditions for the existence of unique coupled common fixed poi... more In this paper, study of necessary conditions for the existence of unique coupled common fixed point of contractive type mappings in the context of two generalized metric spaces is initiated. These results generalize several comparable results from the current literature. We also provide illustrative examples in support of our new results.
Common fixed point theorems for the class of four non compatible mappings in fuzzy metric spaces ... more Common fixed point theorems for the class of four non compatible mappings in fuzzy metric spaces are proved. These results are proved without exploiting the notion of continuity and without imposing any condition on t-norm. * Mathematics Subject Classifications: 54H25,47H10,54E40,54E35.
We use an iteration scheme to approximate common fixed points of nearly asymptotically nonexpansi... more We use an iteration scheme to approximate common fixed points of nearly asymptotically nonexpansive mappings. We generalize corresponding theorems of [1] to the case of two nearly asymptotically nonexpansivemappings and those of [9] not only to a larger class of mappings but also with better rate of convergence.
We prove the existence of fuzzy common fixed point of two mappings satisfying a generalized contr... more We prove the existence of fuzzy common fixed point of two mappings satisfying a generalized contractive condition in complete ordered spaces. Our results provide extension as well as substantial improvements of several well-known results in the existing literature and initiate the study of fuzzy fixed point theorems in ordered spaces.
In this paper, we introduce an iteration scheme for two multivalued maps in Kohlenbach hyperbolic... more In this paper, we introduce an iteration scheme for two multivalued maps in Kohlenbach hyperbolic spaces. This extends the single-valued iteration process due to Agarwal et al. (J. Nonlinear Convex Anal. 8(1):61-79, 2007). Using this new algorithm, we approximate common fixed points of two multivalued mappings through -convergence and strong convergence under some weaker conditions. A necessary and sufficient condition is given for strong convergence. MSC: Primary 47A06; 47H09; 47H10; secondary 49M05
In this paper, we introduce the notion of almost generalized (ψ , ϕ) s -contractive mappings and ... more In this paper, we introduce the notion of almost generalized (ψ , ϕ) s -contractive mappings and we establish some fixed and common fixed point results for this class of mappings in ordered complete b-metric spaces. Our results generalize several well-known comparable results in the literature. Finally, two examples support our results. MSC: 54H25; 47H10; 54E50
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