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In this paper we generalize the notion of O−set and establish some fixed point theorems for ⊥ − α − ψ−contraction multifunction in the setting of orthogonal modular metric spaces. As consequences of these results we deduce some theorems in orthogonal modular metric spaces endowed with a graph and partial order. Finally, we establish some theorems for integral type contraction multifunctions and give some examples to demonstrate the validity of the results.

FIXED POINT OF MULTIVALUED CONTRACTIONS IN ORTHOGONAL MODULAR METRIC SPACES