A coincidence and common fixed point theorem for subsequentially continuous hybrid pairs of maps satisfying an implicit relation

Abstract

Abstract. In this paper, we introduce the notion of subsequential continuity for a hybrid pair of maps and combine this concept with compatibility, to establish a coincidence and common fixed point theorem for a hybrid quadruple of maps. Our main result also demonstrates that several fixed point theorems can be unified using implicit relations. We also give two examples in support our results.

Fixed points for occasionally weakly biased mappings of type (A)

“…According to [24], several classical fixed point theorems and common fixed point theorems have been unified considering a general condition by an implicit relation in ( [22,23]) and in other papers. Motivated by the three cited papers and the next ones [1,2,4,5,11,18,25,26,27] and so on, we introduce the new type of implicit relations.…”

“…Theorem 1. Let f , g, h and k be self-mappings of a metric space X satisfying the following condition ϕ(d(f x, gy), d(hx, ky), d(f x, hx), d(gy, ky), (5) d(hx, gy), d(f x, ky)) ≤ 0, for all x, y ∈ X , where ϕ ∈ Φ. If the pair (f, h) as well as (g, k) is occasionally weakly h-biased of type (A) and occasionally weakly k-biased of type (A), respectively, then f , g, h and k have a unique common fixed point.…”

Fixed Point Theorems for Mappings Satisfying Implicit Relation in Partial Metric Spaces

“…The introduction of implicit relations in common fixed point theorems was established by V. Popa [16] in . Further many authors extended common fixed point theorems using implicit relations ( [17,18,19,20,21]).…”

Fixed point, its geometry, and application via ω‐interpolative contraction of Suzuki type mapping

“…In 1930, Caccioppoli 1 enhanced and improved the conclusions of Banach 2 from normed space to metric space. Following him, numerous authors investigated many abstract spaces to generalize the conclusions of Banach 2 and Caccioppoli, 3 for instance, previous works [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] and references therein. However, all such efforts were not beneficial, which was the main reason for the new explorations.…”