Fixed Points and Continuity for a Pair of Contractive Maps with Application to Nonlinear Volterra Integral Equations

Abstract

In this paper, we have established and proved fixed point theorems for the Boyd-Wong-type contraction in metric spaces. In particular, we have generalized the existing results for a pair of mappings that possess a fixed point but not continuous at the fixed point. We can apply this result for both continuous and discontinuous mappings. We have concluded our results by providing an illustrative example for each case and an application to the existence and uniqueness of a solution of nonlinear Volterra integral equations.

On Solution of Nonlinear Integral and Fractional Differential Equations via Discontinuous Nonlinear Contractions

“…Several other researchers extended these results in diferent directions. One can see the results proved in ( [10][11][12][13][14]) and the references therein. In this continuation, most recently some interesting generalizations of these results were obtained by Karapinar et al [15] and by Prasad ([16,17]).…”

Fixed-Point Theorems for ω − ψ -Interpolative Hardy-Rogers-Suzuki-Type Contraction in a Compact Quasipartial b -Metric Space

“…where Later, Wangwe and Kumar [24] proved results for α − F -type contractions. One can see more results in [25][26][27][28] and the references therein.…”

“…Kumar [27] discussed the concept of orbital continuity. Using this concept, we formulate the following example which validates the result proved in Theorem 28.…”

Fixed Point Results via Real-Valued Function Satisfying Integral Type Rational Contraction

“…These studies further give other aspects of integral contractions for researchers, in particular related problems on real-valued functions. Some motivated results on integral type contractions and in metric spaces are refer to see [11][12][13][14][15][16][17].…”