Some approximate fixed point results and application on graph theory for partial (h-F)-generalized convex contraction mappings with special class of functions on complete metric space

Abstract

In this paper, we introduce a new concept called partial (h-F)-generalized (and (h-F)-subgeneralized) convex contractions of order 3 (and with rank 3) using some auxiliary functions. Also we present some approximate fixed point results in metric space and approximate fixed point results in metric space endowed with a graph. Some examples are provided to illustrate the main results and to show the essentiality of the given hypotheses.

Some approximate fixed point theorems without continuity of the operator using auxiliary functions

“…Then each h is a function of subclass of type I. Definition 2.14 (see [1], [4], [9]). Let h, F : R + × R + → R. Then we say that the pair (F , h) is an upper class of type I if h is a function of subclass of type I and: x i , n ∈ N and F (s, t) = st;…”

Some Common Fixed Points of Six Mappings on G_b-metric Spaces Using (E.A) Property

“…After that several fixed point results were obtained. Among these works, we mention ( [6], [7], [11], [14], [15], [16], [24]- [40]). In 2014, Aghajani et al [2] introduced a new generalization of a metric space.…”

Common fixed point theorems for two pairs of self-mappings in partial metric space using C-class functions on (ψ,φ)-contractive condition

“…In 2014 the concept of C-class functions (see Definition 1.6) was introduced by Ansari in [3]. For more results on common fixed point for different metric spaces see the references [2,[10][11][12][18][19][20][21][22][23][24][25][26][27].…”