An Application of Fixed Point Theory to a Nonlinear Differential Equation
An Application of Fixed Point Theory to a Nonlinear Differential Equation
We introduce a new family of mappings on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mo stretchy="false">[</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mo>+</mml:mo><mml:mi>∞</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>by relaxing the nondecreasing condition on the mappings and by using the properties of this new family we present some fixed point theorems for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>α</mml:mi></mml:mrow></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow></mml:math>-contractive-type mappings in the setting of complete metric spaces. By applying …