Maia type fixed point results via C-class function

Abstract

In 1968, M. G. Maia [16] generalized Banach’s fixed point theorem for a set X endowed with two metrics. In 2014, Ansari [2]introduced the concept of C-class functions and generalized many fixed point theorems in the literature. In this paper, we prove some Maia’s type fixed point results via C-class function in the setting of two metrics space endowed with a binary relation. Our results, generalized and extended many existing fixed point theorems, for generalized contractive and quasi-contractive mappings, in a metric space endowed with binary relation.

Maia type fixed point theorems for some classes of enriched contractive mappings in Banach spaces

“…3. Similar Maia fixed point theorems could be obtained by applying the technique of enriching nonlinear operators for the classes of contractive mappings studied in [1], [4], [5]- [7], [9], [10], [22], [23], [25], [30]- [39], [42], [45]- [87] etc.…”

“…Due to the beautiful idea on which the Maia's fixed point theorem is builded, it attracted much interest and still attracts many researchers working in fixed point theory, see Albu [1], Ansari et al [4], Balazs [5]- [7], Bayen [9], Berinde [10], Berinde and Vetro [22], Bhola and Sharma [23], Bylka [25], Dhage [30]- [33], Dhage and Dhobale [32], Filip [34], [35], Garg [36], Gheorghiu [37], Ilea [38], Iseki [39], Kasahara [42], A. S. Mures ¸an [45], [46], V. Mures ¸an [47]- [50], Nȃdȃban et al [51], Nagare [52], Namdeo and Gupta [53], Pachpatte [54], Pȃcurar [55], [56], Pȃcurar and Rus [57], Pande [58], Pathak and Dubey [59], Petracovici [60], Petrus ¸el and Rus [61], Petrus ¸el et al [62], Popa [63], Precup [64], Ray [65], Rus [68]- [75], Rzepecki [76]- [78], Sharma [79], Shrivastava and Dubey [80], Shukla and Radenović…”