## On monotonic solutions of some functional equations |

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### Contents

INTRODUCTION | 5 |

monotonic solutions of some special linear functional | 30 |

monotonic solutions of the linear functional equation | 48 |

### Common terms and phrases

A\S the function abstract algebras compactly ordered space Compare footnote completes the proof connected set continuous function converges defined and increasing defined by 3.21 defined Q-a.e dense dense set empty set essential supremum exists a function exists an increasing f is continuous follows fulfilled and let fulfils the condition fulfils the equation function h function q>(x functional equation g and h greatest element h is decreasing h is defined Hence increasing function increasing Q-a.e increasing with respect inequality inf h(x infimum interval Kuczma least element let f let g Let hypotheses H2 Let SeQ let xn linearly ordered space lower bound monotonic functions monotonic solutions Moreover neighbourhood non-empty non-negative and decreasing positive integer real numbers satisfies equation 3.1 sequence xn set A0 solution of equation strictly increasing subset of A0 supA Suppose that hypotheses supremum Theorem 2.1 topology upper bound virtue of Lemma xeA\S xeA0 xeAl