Fixed point theorems for generalized weakly contractive mappings

Fixed point theorems for hybrid contraction without continuity

“…In this paper we will establish a fixed point theorems under generalized weak contractive condition for a pair of multi-valued and single-valued mappings by using the concept of (IT)-commutativity of mappings in complete metric space without appeal to continuity of mappings. Our results extend and generalize the results of Choudhury et al [6] and others.…”

“…Subsequently Rhoades [26] use the notion of weakly contractive mappings and obtained a fixed point theorem in complete metric space. Afterward, weak contraction and function satisfying weak contractive type inequalities have been considered in a large number of papers, (see, for instance [1], [2], [6], [7], [11], [25] and references therein). In this paper we will establish a fixed point theorems under generalized weak contractive condition for a pair of multi-valued and single-valued mappings by using the concept of (IT)-commutativity of mappings in complete metric space without appeal to continuity of mappings.…”

“…Definition 2.7. [6] : Let (X, d) be a metric space, f a self mapping of X. We shall call f a generalized weakly contractive mapping if for all x, y ∈ X…”

“…[6] : Let (X, d) be a complete metric space, and let f : X → X be such that Proof. Let x 0 be an arbitrary point in X.…”

Existence of a common solution for a system of nonlinear integral equations via fixed point methods inb-metric spaces

“…In 2011, Choudhury et al [9] generalized the concept of weak contraction mappings by using an altering distance function and proved fixed point theorem for such mappings. Recently, Roshan et al [10] studied some coincidence point results for four mappings satisfying generalized weak contractive conditions in the framework of partially ordered b-metric spaces (b-metric spaces in the sense of Czerwik [11]).…”