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We introduce the new type of nonself mapping and study sufficient conditions for the existence of past-present-future (for short PPF) dependent fixed point for such mapping in the Razumikhin class. Also, we apply our result to prove the PPF dependent coincidence point theorems. Finally, we use PPF dependence techniques to obtain solution for a nonlinear integral problem with delay. [ABSTRACT FROM AUTHOR]

We study Ulam-Hyers stability and the well-posedness of the fixed point problem for new type of generalized contraction mapping, so called α-λ-contraction mapping. The results in this paper generalize and unify several results in the literature such as the Banach contraction principle. [ABSTRACT FROM AUTHOR]

Recently, Basha (2011) established the best proximity point theorems for proximal contractions of the first and second kinds which are extension of Banach's contraction principle in the case of non-self-mappings. The aim of this paper is to extend and generalize the notions of proximal contractions of the first and second kinds which aremore general than the notion of self-contractions, establish the existence of an optimal approximate solution theorems for these non-self-mappings, and also give examples to validate ourmain results. [ABSTRACT FROM AUTHOR]

We introduce two new concepts of weakly relaxed η-α monotone mappings and weakly relaxed η-α semimonotone mappings. Using the KKM technique, the existence of solutions for variational-like problems with weakly relaxed η-α monotone mapping in reflexive Banach spaces is established. Also, we obtain the existence of solution for variational-like problems with weakly relaxed η-α semimonotone mappings in arbitrary Banach spaces by using the Kakutani-Fan-Glicksberg fixed-point theorem. [ABSTRACT FROM AUTHOR]

We introduce the concept of the generalized wα-contraction mappings and establish the existence of fixed point theorem for such mappings by using the properties of w-distance and α-admissible mappings. We also apply our result to coincidence point and common fixed point theorems in metric spaces. Further, the fixed point theorems endowed with an arbitrary binary relation are also derived from our results. Our results generalize the result of Kutbi, 2013, and several results in the literature. [ABSTRACT FROM AUTHOR]

We extend the recent results of the coupled fixed point theorems of Cho et al. (2012) by weakening the concept of the mixed monotone property. We also give some examples of a nonlinear contraction mapping, which is not applied to the existence of the coupled fixed point by the results of Cho et al. but can be applied to our results. The main results extend and unify the results of Cho et al. and many results of the coupled fixed point theorems. [ABSTRACT FROM AUTHOR]

The objective of this paper is to emphasize the role of "common limit range property" to ascertain the existence of common fixed point in fuzzy metric spaces. Some illustrative examples are furnished which demonstrate the validity of the hypotheses and degree of utility of our results. We derive a fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. As an application to ourmain result, we prove an integraltype fixed point theorem in fuzzy metric space. Our results improve and extend a host of previously known results including the ones contained in Imdad et al. (2012). [ABSTRACT FROM AUTHOR]

We introduce the notion of generalized α*-admissible mappings. By using this notion, we prove a fixed point theorem. Our result generalizes Mizoguchi-Takahashi's fixed point theorem. We also provide some examples to show the generality of our work. [ABSTRACT FROM AUTHOR]

We give some initial properties of a subset of modular metric spaces and introduce some fixedpoint theorems for multivalued mappings under the setting of contraction type. An appropriate example is as well provided. The stability of fixed points in our main theorems is also studied. [ABSTRACT FROM AUTHOR]

The aim of this paper is to obtain some new integral type fixed point theorems for nonself weakly compatible mappings in symmetric spaces satisfying generalized (ψ, φ)-contractive conditions employing the common limit range property We furnish some interesting examples which support our main theorems. Our results generalize and extend some recent results contained in Imdad et al. (2013) to symmetric spaces. Consequently, a host of metrical common fixed theorems are generalized and improved. In the process, we also derive a fixed point theorem for four finite families of mappings which can be utilized to derive common fixed point theorems involving any number of finite mappings. [ABSTRACT FROM AUTHOR]