Coincidence and fixed points of nonlinear Hybrid contractions

Coincidence Theorem for Multi-Valued and Single-Valued Systems of Transformations

“…For n = 1, this definition is that of Kaneko [9] (see, Singh et al [23]). Two systems are coordinate wise weakly commuting on X if and only if they are co-ordinatewise weakly commuting at every point of X.…”

“…Replacing the co-ordinatewise R-weakly commuting condition in Theorem 3.1 by co-ordinatewise weakly commuting we get the result of Baillon-Singh [1], REMARK 3.2. The result of corollary 3.1 includes a multitude of contrative condition for single and multi-valued maps (see, for instance [2], [5], [6], [9], [11], [13], [14], [17], [18], [19], [21], [22], [23] and [25]). The following result is corollary 3.1 with (Y, d) = (Xi,di), P = Pi, Q = Qi, i = l,...,n and n = 1, max{an,b} = k (say).…”

Fixed point theorems for hybrid contraction without continuity

“…Subsequently a number of fixed point theorems in metric space have been proved for multi-valued mapping satisfying contractive type conditions (see, for instance [8], [9], [18], [20], [32] and references therein). Later on the study of hybrid fixed point theory for nonlinear single-valued and multi-valued mappings is a new development in the domain of contractive type multi-valued theory( see, for instance [4], [5], [12], [17], [21], [24], [28], [29], [30], [31], [33], [34] and references therein). On the other hand Alber and Guerre-Delabriere [3], defined weakly contractive mappings on a Hilbert space and established a fixed point theorem for such a mappings.…”

Coincidence and Fixed Point for Weakly Reciprocally Continuous Single-Valued and Multi-Valued Maps

“…Pant [9] initiated the study of noncompatibilty by introducing point wise R-weak commutativity. Shahzad and Kamran [15], and Singh and Mishra [16], independently, extended the idea of R-weak commutativity for a hybrid pair of single and multi-valued maps. Kamran [5] extended the concept of R-weak commutativity of type A g [11] for multivalued maps and introduced R-weakly commuting mappings of type A T .…”