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The fixed point theorems for one mapping and the common fixed point theorems for two mappings satisfying generalized Lipschitz conditions are obtained, without appealing to continuity for mappings or normality for cone in the conditions. Furthermore, we not only get the existence of the fixed point but also get the uniqueness. These results greatly improve and generalize several well-known comparable results in the literature. Moreover, example is given to support our new results.

journal of function spaces

Some New Theorems on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:math>-Distance without Continuity in Cone Metric Spaces over Banach Algebras

Some New Theorems on c-Distance without Continuity in Cone Metric Spaces over Banach Algebras