We introduce the concepts  of <mml:math alttext="$\ast$" id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>&#x2217;</mml:mo></mml:math>-diminishing orbital diameters and diminishing orbital diameters for a pair <mml:math alttext="$(f,g)$" id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>f</mml:mi><mml:mo>,</mml:mo><mml:mi>g</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math> of self mappings in  metric spaces and prove common fixed point
theorems for these mappings. The results obtained in this paper
extend properly the result of Fisher (1978).

International Journal of Mathematics and Mathematical Sciences

On mappings with diminishing orbital diameters

Abstract

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