Some new fixed point results in partial ordered metric spaces via admissible mappings

Abstract

The purpose of this paper is to discuss the existence of fixed points for new classes of mappings defined on an ordered metric space. The obtained results generalize and improve some fixed point results in the literature. Some examples show the usefulness of our results. MSC: 46N40; 47H10; 54H25; 46T99

Some new fixed point results in partial ordered metric spaces via admissible mappings and two new functions

“…That is, the contractive condition of Theorem 2.1 in ( [33]) does not hold for this example. (4) Taking F , h, f , take h(x, y, z) = xyz, F (s, t) = st, f (s, t) = s − t, we have actually [33,Theorem 2.7].…”

“…We will illustrate the example to show that our contractions is weaker than that in [33]. The condition can be applied to Theorem 1.14, but not applied to [33, Theorem 2.1].…”

“…(5) When h(x, y, z) = (xy + l) z , l > 0, F (s, t) = (1 + l) st , f (s, t) = s − t and l = 1, Theorem 1.14 can reduce to [33,Corollary 2.9]. …”

“…[33]. Our contraction can be reduced to that in [33]. Indeed, [33, Theorem 2.1] is taken as a particular case of Theorem 1.14.…”

“…(4) Taking F , h, f , take h(x, y, z) = xyz, F (s, t) = st, f (s, t) = s − t, we have actually [33,Theorem 2.7].…”