Fixed‐point theorems for weak ( ψ ,  β )‐mappings satisfying generalized C ‐condition and its application to boundary value problem

Abstract

In this paper, we define a generalized C‐condition and prove a fixed‐point theorem for weak (ψ,β)‐contraction in partially ordered metric spaces. Our result extends the result of Suzuki (Proc. of the 8th Int. Conf. of Fixed Point Theory and Its Appl. 2007;65:751‐761) and Gupta and Mani (Funct Anal Theory Methods Appl. 2017;3:26‐34). As an application, existence and uniqueness of solution of first‐order periodic boundary value problem have been given in support of our finding.

Fixed point theorem for new type of auxiliary functions

“…Taking limit as p → ∞ in equality (14) and using equations (15), (16), (17), (18) and (19) all together in (14), we get…”

“…Some other results in complete metric spaces satisfying integral type contractions are mentioned in [8,9,11,12,13,17,18] In 2014-15, Ansari [1] introduced the notion of C -class function as a major generalization of Banach contraction principle. Currently this finding is one of the most attractive research topics in fixed point theory.…”

Maia type fixed point results via C-class function

“…By using this concept we can generalize many fixed point theorems in the literature. C-class functions have been studied by many authors.and some fixed point results with applications (see eg., [3,12,18,4,13]).…”

Cyclic G ‐ Ω -Weak Contraction-Weak Nonexpansive Mappings and Some Fixed Point Theorems in Metric Spaces

“…Fixed point theorems corresponding to these types of contraction mappings have many applications, not exclusively; see [22,23] and also see the applications of the prior results given via the references mentioned in these research papers.…”