Quanita Kiran

Fixed point theorems for multi-valued mappings obtained by altering distances

Abstract Recently T. Suzuki showed that the Mizoguchi–Takahashi fixed point theorem is a real generalization of Nadler’s fixed point theorem. Taking inspiration from the result of Mizoguchi and Takahashi and using the ideas of Feng and Liu, Klim and Wardowski obtained some fixed point theorems and showed that their results are different from the Reich point theorem and the Mizoguchi–Takahashi fixed point theorem. Very recently, Pathak and Shahzad introduced a class of functions and generalized some fixed point theorems of Klim and Wardowski by altering distances, i.e., via the mapping T (from a complete metric space ( X , d ) to the class of nonempty closed subsets of X ). In this paper we introduce a new class of functions which is a subclass of the class introduced by Pathak and Shahzad and improve some results of Pathak and Shahzad by allowing T to have values in closed subsets of X .

Fixed Point Theorems for Multivalued Mappings Involving -Function

We obtain some fixed point theorems with error estimates for multivalued mappings satisfying a new --contractive type condition. Our theorems generalize many existing fixed point theorems, including some fixed point theorems proved for --contractive type conditions.

Generalization of Mizoguchi-Takahashi type contraction and related fixed point theorems

In this paper, we introduce a new notion to generalize a Mizoguchi-Takahashi type contraction. Then, using this notion, we obtain a fixed point theorem for multivalued maps. Our results generalize some results by Minak and Altun, Kamran and those contained therein.MSC:47H10, 54H25.

Fixed point theorems for φ-contractions

This paper deals with the fixed point theorems for mappings satisfying a contractive condition involving a gauge function φ when the underlying set is endowed with a b-metric. Our results generalize/extend the main results of Proinov and thus we obtain as special cases some results of Mysovskih, Rheinboldt, Gel’man, and Huang. We also furnish an example to substantiate the validity of our results. Subsequently, an existence theorem for the solution of initial value problem has also been established.MSC:47H10, 54H25.

FIXED POINT AND HOMOTOPY RESULTS FOR GENERALIZED CONTRACTIONS ON SPACES WITH TWO METRICS

In this paper, we establish fixed point and homotopic results for generalized contractions on spaces with two metrics. Our results generalize and extend the results of Agarwal and O’Regan [R. P. Agarwal, Donal O’Regan, Fixed point theory for generalized contractions on spaces with two metrics, J. Math. Anal. Appl. 248(2000), 402-414] and those contain therein.