A New Best Proximity Point Result with an Application to Nonlinear Fredholm Integral Equations

Abstract

In the current paper, we first introduce a new class of contractions via a new notion called p-cyclic contraction mapping by combining the ideas of cyclic contraction mapping and p-contraction mapping. Then, we give a new definition of a cyclically 0-complete pair to weaken the completeness condition on the partial metric spaces. Following that, we prove some best proximity point results for p-cyclic contraction mappings on D∪E where D,E is a cyclically 0-complete pair in the setting of partial metric spaces. Hence, we generalize and unify famous and well-known results in the literature of metric fixed point theory. Additionally, we present some nontrivial examples to compare our results with earlier. Finally, we investigate the sufficient conditions for the existence of a solution to nonlinear Fredholm integral equations by the results in the paper.

Proximity Point Results for Generalized p-Cyclic Reich Contractions: An Application to Solving Integral Equations

“…The obtained results generalize and extend certain well-known findings in metric fixedpoint theory, which include results of Eldred-Veeremani [17], Popescu [3], and Sahin [16]. First, we introduce the concept of p-cyclic Reich contraction by combining the concepts of cyclic contraction and p-contraction.…”

“…Since from the assumption, ( , ℵ) is a cyclically complete pair in U, either µ n or ω m converges. Assume that the sequence µ n converges in , so there exists µ ∈ such that Finally, it follows from Equations ( 4), (16), and (17) that ρ(µ, ω) = lim n,s→∞ ρ(µ n , ω m s ) = ρ( , ℵ).…”

Solution of Nonlinear Fredholm Integral Equations on Almost Z ⊥ -Contraction

“…Kumari Panda et al [18] achieved some fxed point fndings and proposed a very easy solution for a Volterra integral problem utilizing the fxed point approach in the situation of dislocated extended b-metric space. Sahin [19] introduced a pcyclic contraction mapping by combining the ideas of cyclic contraction mapping and p-contraction mapping and investigated the sufcient conditions for the existence of a solution to nonlinear Fredholm integral equations.…”

The Best Proximity Point Problem for New Types of Ciric a 􀀀b􀀀 Contraction with Application

“…Anuradha and Veeramani (6) proved the existence of a best proximity point for proximal pointwise contraction. Recently many authors have studied and generalize various concept related to the best proximity points (7)(8)(9)(10)(11)(12)(13)(14) .…”