Extensions of a fixed point theorem of Meir and Keeler

Compatible mappings and common fixed points (2)

“…The utility of compatibility in the context of fixed point theory was demonstrated by extending a theorem of Park and Bae [2] The purpose of this note is to further emulate the compatible map concept.…”

Suzuki type common fixed point theorem in complete metric space and partial metric space

“…The concept of compatible mappings was introduced by Jungck [12] as a generalization of commuting mappings. The utility of compatibility in the context of fixed point theory was demonstrated by extending a theorem of Park-Bae [25]. Recently Samet et al [27] introduced a definition of compatible pair of mappings in partial metric spaces.…”

Some Fixed Point Theorems on Meir Keeler Type under Strict Contractions

“…The most general form of the common fixed point theorem pertaining to four mappings A, B, S and T of a metric space (X, (ii) (t) is non decreasing, for each t > 0, lim ( ) n n t = 0 which implies that (t) < t. (Jachymski [7]) (iii) (t) is upper semi continuous (Boyd and Wong [5], Jachymski [7], Pant [16]) (iv) (t) is non decreasing, right continuous and (t) < t for every t > 0. ( Park and Rhoades [19])…”