School of Mathematics & Computer Application

In the present article, the notion of αH-ψH-multivalued contractive type mappings is introduced and some fixed point results in complete metric spaces are studied. These theorems generalize Nadler’s (Multivalued contraction mappings, Pac. J. Math., 30, 475–488, 1969) and Suzuki-Kikkawa's (Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal., 69, 2942–2949, 2008) results that exist in the literature. The effectiveness of the obtained results has been verified with the help of some comparative examples. Moreover, a homotopy result has been presented as an application.

In the present work, the concept of F-generalized contractive type mappings by using C-class functions is introduced, and some common fixed point results for weakly isotone increasing set-valued mappings in the setting of ordered partial metric spaces are studied. These results improve and generalize various results existing in the literature. The effectiveness of the obtained results is verified with the help of some comparative examples.

In the present work, the concept of F-generalized contractive type mappings by using C-class functions is introduced, and some common fixed point results for weakly isotone increasing set-valued mappings in the setting of ordered partial metric spaces are studied. These results improve and generalize various results existing in the literature. The effectiveness of the obtained results is verified with the help of some comparative examples.

In the present paper, we extend the concept of contraction in a new manner by introducing D-contraction defined on a family F of bounded functions. We also introduce a new notion of a fixed function on a metric space. Some fixed function theorems along with illustrative examples and application are also given to verify the effectiveness of our results.

In the present article, the concept of expansion is extended in a refined manner by introducing P-expansion defined on a family F of bounded functions. Some fixed function theorems using expansive mappings in complete metric spaces are investigated. These results improve and generalize various results existing in literature. The authenticity of obtained results is verified with the help of some comparative examples. In addition, an application has also been presented which is based on the best approximation of dose distribution for a number of patients (at a same time) getting Tomotherapy.

In the present paper, the concept of contraction has been extended in a refined manner by introducing $\mathfrak{D}$-Contraction defined on a family $\mathfrak{F}$ of bounded functions. Also, a new notion of fixed function has been introduced for a metric space. Some fixed function theorems along with illustrative examples have also been given to verify the effectiveness of our results. In addition, an application to medical science has also been presented. This application is based on best approximation of treatment plan for tumor patients getting intensity modulated radiation therapy(IMRT). In this technique, a proper DDC matrix truncation has been used that significantly improves accuracy of results. In 2013, Z. Tian \textit{et al.} presented a fluence map optimization(FMO) model for dose calculation by splitting the DDC matrix into two components on the basis of a threshold intensity value. Following this concept, a sequence of functions can be constructed through the presented ...